Back to the roots of data-driven dynamical system identification

A Recursive Algorithm to Compute a Numerical Basis of the Null Space of the Block Macaulay Matrix

Author(s): Vermeersch, Christof; De Moor, Bart
Published in: Proc. of the 29th ERNSI Workshop in System Identification (ERNSI21);, Issue 2021, 2021
Publisher: ERNSI

Multivariate Polynomials (with MacaulayLab) for Beginners

Author(s): Vermeersch, Christof; De Moor, Bart
Published in: Open Flanders AI Research Day, 2023/10/16 - 2023/10/16, 2023
Publisher: KU Leuven

Globally optimal least-squares misfit identification of multidimensional autonomous systems

Author(s): Vanpoucke, Lukas; De Moor, Bart
Published in: 30th ERNSI Workshop in System Identification (ERNSI 2022), 2022
Publisher: KU Leuven

Realizing first-order polynomial state-space models: Using a linear algebraic framework

Author(s): De, Sarthak, De Moor, Bart
Published in: 33rd ERNSI Workshop on System Identification, Bourdeaux, France, 2025
Publisher: KU Leuven

Multiparameter eigenvalue problems

Author(s): De Moor, Bart
Published in: XXI Householder Symposium on Numerical Linear Algebra, Issue 2022-06;, 2022
Publisher: Householder Symposium on Numerical Linear Algebra

Globally optimal SISO H2-norm model reduction

Author(s): Lagauw S., De Moor B.
Published in: Poster Presentation: Selma Closing Event, 2022/06/14 - 2022/06/14, 2023
Publisher: KU Leuven

Using the (Block) Macaulay Matrix in the Chebyshev Polynomial Basis

Author(s): Vermeersch, Christof; De Moor, B
Published in: ERNSI 2023, 2023/09/24 - 2023/09/27,, 2023
Publisher: KU Leuven

State Elimination in Polynomial Models : A Linear Algebraic Approach

Author(s): De S., De Moor B
Published in: Technical Report 25-163, ESAT-STADIUS, KU Leuven, 2025
Publisher: KU Leuven

About the Fundamental Subspaces of the Macaulay Matrix

Author(s): Christof Vermeersch, Bart De Moor
Published in: 6th Conference on Applied Algebraic Geometry (AG23),, 2023
Publisher: KU Leuven

Least squares optimal realisation of SISO LTI systems is an eigenvalue problem

Author(s): Lagauw, Sibren; De Moor, Bart
Published in: 30th ERNSI Workshop in System Identification (ERNSI22),, Issue 2022, 2022
Publisher: https://kuleuven.limo.libis.be/discovery/fulldisplay?docid=lirias4020036&context=SearchWebhook&vid=32KUL_KUL:Lirias&lang=en&search_scope=lirias_profile&adaptor=SearchWebhook&tab=LIRIAS&query=any,contains,LIRIAS4020036&offset=0

Misfit identification of autonomous multidimensional systems

Author(s): Vanpoucke, L; De Moor, Bart
Published in: 41st Benelux Meeting on Systems and Control, Issue 2022, 2022
Publisher: Meeting on Systems and Control

Exploiting the Macaulay matrix structure for the globally optimal identification of autonomous systems

Author(s): Vanpoucke, L; Lagauw, S; De Moor, Bart
Published in: 32nd ERNSI Workshop on System Identification, 2024
Publisher: KU Leuven

Globally optimal least squares misfit identification of multidimensional, autonomous, linear, shift-invariant systems

Author(s): Vanpoucke L., De Moor B.
Published in: Technical Report 26-24, ESAT-STADIUS, KU Leuven, 2026
Publisher: KU Leuven

Global Identifiability of parameterized nonlinear dynamical models'

Author(s): De S., De Moor B.
Published in: 31st ERNSI Workshop in System Identification (ERNSI 2023), Stockholm, Sweden, 2023
Publisher: KU Leuven

Porteous Meets Walsh: Counting Critical Points for H2-Norm Model Reduction Using Algebraic Geometry Behind Multiparameter Eigenvalue Problems

Author(s): Lagauw S., Kayser L., De Moor B.
Published in: Technical Report 26-30, ESAT-STADIUS, KU Leuven, 2026
Publisher: KU Leuven

Globally optimal misfit identification of multidimensional difference equations

Author(s): Vanpoucke, Lukas; De Moor, Bart
Published in: 31st ERNSI Workshop in System Identification (ERNSI 23), 2023
Publisher: KU Leuven

Least-squares globally optimal misfit modelling for SISO systems

Author(s): Lagauw, Sibren; De Moor, Bart
Published in: 41st Benelux Meeting on Systems and Control, Issue 2022, 2022
Publisher: Benelux meeting on Systems and Control

Multivariate polynomials and autonomous, scalar, linear, shiftinvariant models of finite order

Author(s): Vanpoucke L., De Moor B.,
Published in: Technical Report 26-25, ESAT-STADIUS, KU Leuven, 2026
Publisher: KU Leuven

Connection Between DTLS as an MEVP and as a Riemannian SVD

Author(s): Viroux, Sem; De Moor, Bart
Published in: 42nd Benelux Meeting on Systems and Control, 2023
Publisher: KU Leuven

The Cuckoo Problem: Finding the Globally Optimal Critical Value of a Polynomial Optimization Problem using the Macaulay Matrix

Author(s): van Rooij H., De Moor B.
Published in: 32nd ERNSI workshop on system identification, Venice, Italy, 2024
Publisher: KU Leuven

Numerical elimination theory via the Macaulay matrix

Author(s): van Rooij H., De Moor B.
Published in: Technical Report 26-39, ESAT-STADIUS, KU Leuven, 2026
Publisher: KU Leuven

Using the Macaulay Matrix to find the Globally Optimal Critical Value of a Multivariate Polynomial Optimization Problem

Author(s): van Rooij H., De Moor B.
Published in: Benelux Meeting on Systems and Control 2024 (Benelux Meeting 2024), Blankenberge, Belgium, 2024
Publisher: KU Leuven

Exploring the Critical Values of Multivariate Polynomial Optimization Problems in System Identification Applications

Author(s): van Rooij, Hans; De Cock, Katrien; De Moor, Bart
Published in: 31st ERNSI Workshop in System Identification (ERNSI 23), 2023/09/24 - 2023/09/27, 2023
Publisher: KU Leuven

Connection Between DTLS as an MEVP and as a Riemannian SVD

Author(s): Viroux, Sem; De Moor, Bart
Published in: 42nd Benelux Meeting on Systems and Control (BENELUX23), 2023
Publisher: KU Leuven

Exploiting Shift-Invariant Subspaces

Author(s): Vermeersch, C. ; De Cock, K. ; De Moor, B.
Published in: Poster presentation at the SeLMA Closing Event, Issue 2022, 2022
Publisher: KU Leuven

Generic and specific Euclidean distance degrees of secant varieties to the rational normal curve

Author(s): Kayser L., Lagauw S., De Moor B.,
Published in: Technical Report 26-31, ESAT-STADIUS, KU Leuven (Leuven, Belgium, 2026
Publisher: KU Leuven

Elimination in polynomial state-space models - Using the SVD to compute output difference equations

Author(s): De S., De Moor B.
Published in: 32nd ERNSI workshop in system identification (ERNSI 2024 ), Venice, Italy, 2024
Publisher: KU Leuven

Using Numerical Elimination Theory for Polynomial Optimization with Positive-Dimensional Solution Sets

Author(s): van Rooij H., De Moor B.
Published in: 33rd ERNSI Workshop on System Identification, Bordeaux, France, 2025
Publisher: KU Leuven

System Identification Problems as Multiparameter Eigenvalue Problems

Author(s): Vermeersch, C; De Moor, Bart
Published in: 30th ERNSI Workshop in System Identification (ERNSI 2022), Issue 2022, 2022
Publisher: KU Leuven

Globally optimal least-squares misfit identification of multidimensional autonomous systems

Author(s): Vanpoucke, Lukas; De Moor, Bart
Published in: Poster Presentation: Selma Closing Event, 2022/06/14 - 2022/06/14, 2022
Publisher: KU Leuven

About (Rectangular) Multiparameter Eigenvalue Problems

Author(s): Christof Vermeersch, Bart De Moor
Published in: 42nd Benelux Meeting on Systems and Control (BENELUX23), 2023
Publisher: KU Leuven

Globally optimal SISO H2-norm model reduction

Author(s): Lagauw, Sibren; De Moor, Bart
Published in: 42nd Benelux Meeting on Systems and Control, 2023/03/21 - 2023/03/23,, 2023
Publisher: KU Leuven

On the Rectangular Multiparameter Eigenvalue Problem

Author(s): Vermeersch C., De Moor B
Published in: Technical Report 25-89, ESAT-STADIUS, KU Leuven, 2025
Publisher: KU Leuven

Solving Multivariate Polynomial Systems and Rectangular Multiparameter Eigenvalue Problems with MacaulayLab

Author(s): Vermeersch C., De Moor B.
Published in: Technical Report 25-90, ESAT-STADIUS, KU Leuven, 2025
Publisher: KU Leuven

Subspace Methods for the Block Macaulay Matrix Framework

Author(s): De, Sarthak; Vermeersch, C; De Moor, Bart
Published in: 42nd Benelux Meeting on Systems and Control (BENELUX23), 2023
Publisher: KU Leuven

Globally Optimal Parameter Estimation for Autonomous Nonlinear Dynamical Models is an Eigenvalue Problem

Author(s): De S., De Moor B.
Published in: 43rd Benelux Meeting on Systems and Control, Blankenberge, Belgium, 2024
Publisher: KU Leuven

Low-rank tensor recovery for Jacobian-based Volterra identification of parallel Wiener-Hammerstein systems

Author(s): Usevich, K; Dreesen, P ; Ishteva, M
Published in: IFAC-PapersOnLine, Issue 2021; Vol. 54; iss. 7, 2021, Page(s) 709 - 714, ISSN 2405-8963
Publisher: Elsevier
DOI: 10.1016/j.ifacol.2021.08.403

A Column Space Based Approach to Solve Systems of Multivariate Polynomial Equations

Author(s): Vermeersch, Christof ; De Moor, B
Published in: IFAC-PapersOnLine, Special Issue: 24th International Symposium on Mathematical Theory of Networks and Systems MTNS 2020: Cambridge, United Kingdom,, Issue 2021; Vol. 54, no. 9, 2021
Publisher: IFAC Secretariat
DOI: 10.1016/j.ifacol.2021.06.144

Data-driven simulation for NARX systems

Author(s): Mishra, V; Fazzi, A; Markovsky, I; Dreesen, P
Published in: Proceedings of 29th European Signal Processing Conference (EUSIPCO), Issue 2021, 2021, Page(s) 1055 - 1059, ISBN 978-9-0827-9706-0
Publisher: EURASIP
DOI: 10.23919/eusipco54536.2021.9616226

Globally Optimal H2-norm Model Order Reduction: A Numerical Linear Algebra Approach

Author(s): Agudelo Manozca, Oscar Mauricio; Vermeersch, Christof; De Moor, Bart
Published in: IFAC-PapersOnLine, Special Issue: 24th International Symposium on Mathematical Theory of Networks and Systems MTNS 2020: Cambridge, United Kingdom,, Issue 2021; Vol. 54, no. 9, 2021, Page(s) pp. 564 - 571
Publisher: IFAC Secretariat
DOI: 10.1016/j.ifacol.2021.06.117

Parameter estimation of parallel Wiener-Hammerstein Systems by Decoupling their Volterra Representations

Author(s): Dreesen, Philippe; Ishteva, M
Published in: IFAC-PapersOnLine, Issue 2021; Vol. 54; iss. 7,, 2021, ISSN 2405-8963
Publisher: Elsevier Ltd
DOI: 10.1016/j.ifacol.2021.08.402

Multivariate Polynomial Optimization in Complex Variables Is a (Rectangular) Multiparameter Eigenvalue Problem

Author(s): Christof Vermeersch, Sibren Lagauw, Bart De Moor
Published in: Proc. Of the 62nd Conference on Decision and Control (CDC), 2023
Publisher: Conference on Decision and Control

Exact Characterization of the Global Optima of Least Squares Realization of Autonomous LTI Models as a Multiparameter Eigenvalue Problem

Author(s): Sibren Lagauw, Lukas Vanpoucke, Bart De Moor
Published in: 2024 European Control Conference (ECC), 2024, Page(s) 3446-3451
Publisher: IEEE
DOI: 10.23919/ecc64448.2024.10591182

Multiparameter Eigenvalue Problems and Shift-invariance

Author(s): De Cock, Katrien ; De Moor, Bart
Published in: IFAC-PapersOnLine, Special Issue: 24th International Symposium on Mathematical Theory of Networks and Systems MTNS 2020: Cambridge, United Kingdom,, Issue 2021; Vol. 54, no. 9, 2021, ISSN 2405-8963
Publisher: Elsevier
DOI: 10.1016/j.ifacol.2021.06.071

Two-dimensional descriptor systems

Author(s): Vergauwen, Bob; De Moor, Bart
Published in: IFAC-PapersOnLine, Special Issue: 24th International Symposium on Mathematical Theory of Networks and Systems MTNS 2020: Cambridge, United Kingdom,, Issue 2021; Vol. 54, no. 9, 2021
Publisher: IFAC Secretariat
DOI: 10.1016/j.ifacol.2021.06.070

Incorporating Fixed Pole Information in the Data-Driven Least Squares Realization Problem

Author(s): Christof Vermeersch, Sibren Lagauw, Bart De Moor
Published in: Proceedings of the American Conference on Control (ACC), 2026
Publisher: American Automatic Control Council (AACC)

The (Block) Macaulay Matrix: Solving Systems of Multivariate Polynomial Equations and Multiparameter Eigenvalue Problems

Author(s): Christof Vermeersch
Published in: 2023
Publisher: KU Leuven

Global Solution to Problems in System Identification and Model Order Reduction

Author(s): Lagauw, Sibren
Published in: 2026
Publisher: KU Leuven

Two Complementary Block Macaulay Matrix Algorithms to Solve Multiparameter Eigenvalue Problems

Author(s): Vermeersch, Christof; De Moor, Bart
Published in: Linear Algebra And Its Applications, Issue 2022; Vol. 654, 2022, Page(s) 177 - 209, ISSN 0024-3795
Publisher: Elsevier BV
DOI: 10.1016/j.laa.2022.08.014

Two Double Recursive Block Macaulay Matrix Algorithms to Solve Multiparameter Eigenvalue Problems

Author(s): Christof Vermeersch; Bart De Moor
Published in: IEEE Control Systems Letters, 2022, ISSN 2475-1456
Publisher: IEEE
DOI: 10.1109/lcsys.2022.3182632

Exact solution to the least squares realization problem as a multiparameter eigenvalue problem

Author(s): Sibren Lagauw, Lukas Vanpoucke, Bart De Moor
Published in: Automatica, Issue 185, 2026, Page(s) 112792, ISSN 0005-1098
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.automatica.2025.112792

Least Squares Realization of Complex-Valued Multiple-Output Autonomous LTI Systems via the Riemannian Singular Value Decomposition<sup>*</sup>

Author(s): Sem Viroux, Sibren Lagauw, Bart De Moor
Published in: IEEE Control Systems Letters, Issue 9, 2025, Page(s) 2181-2186, ISSN 2475-1456
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
DOI: 10.1109/lcsys.2025.3604015

Cepstral Identification of Autoregressive Systems

Author(s): Lauwers, Oliver ; Vermeersch, Christof ; De Moor, Bart
Published in: Automatica, Issue 2022; Vol. 139, 2022, ISSN 0005-1098
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.automatica.2022.110214

Globally Optimal SISO H<sub>2</sub>-Norm Model Reduction Using Walsh’s Theorem

Author(s): Sibren Lagauw; Oscar Mauricio Agudelo; Bart De Moor
Published in: IEEE Control Systems Letters, Issue 2023; Vol. 7;, 2023, Page(s) 1670 - 1675, ISSN 2475-1456
Publisher: IEEE
DOI: 10.1109/lcsys.2023.3276299

Recursive Algorithms to Update a Numerical Basis Matrix of the Null Space of the Block Row, (Banded) Block Toeplitz, and Block Macaulay Matrix

Author(s): Christof Vermeersch; Bart De Moor
Published in: SIAM Journal on Scientific Computing, Issue 2023; Vol. 45; iss. 2, 2023, Page(s) A596 - A620, ISSN 1064-8275
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m1495858

Least Squares Projection Onto the Behavior for SISO LTI Models

Author(s): S. Lagauw, B. De Moor
Published in: IFAC-PapersOnLine, Issue 58, 2024, Page(s) 336-341, ISSN 2405-8963
Publisher: Elsevier BV
DOI: 10.1016/j.ifacol.2024.08.551

Constructing Multidimensional Difference Equations From a State-Space Representation Using the Generalized Cayley–Hamilton Theorem

Author(s): Lukas Vanpoucke, Bart De Moor
Published in: IEEE Control Systems Letters, Issue 8, 2024, Page(s) 2259-2264, ISSN 2475-1456
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
DOI: 10.1109/lcsys.2024.3411835

Solving Systems of Polynomial Equations - A Tensor Approach

Author(s): Ishteva, M; Dreesen, P
Published in: Lecture Notes in Computer Science, Issue 2022; Vol. 13127, 2021, Page(s) 333 - 341, ISBN 978-3-030-97548-7
Publisher: Springer
DOI: 10.1007/978-3-030-97549-4_38

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